The Attribution Impossibility: No Feature Ranking Is Faithful, Stable, and Complete Under Collinearity

2026-05-23 · Source: cs.LG updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Software Development & Engineering · Depth: Expert, extended

Summary

A new theorem, "The Attribution Impossibility," proves that no feature ranking can be simultaneously faithful, stable, and complete when features are collinear. This mathematical inevitability means that for correlated feature pairs, rankings often reduce to a coin flip across different model training runs. The research quantifies this impossibility for four model classes, showing the attribution ratio diverges as 1/(1-ρ²) for gradient boosting and is infinite for Lasso. It identifies two method families: unstable faithful-complete methods (up to 50% flip rate) and stable ensemble methods like Dash, which report ties for symmetric features. Dash, a SHAP ensemble averaging technique, is provably Pareto-optimal, achieving the Cramér–Rao variance bound. A survey of 77 public datasets found 68% exhibit this instability, with implications for fairness audits, which are deemed unreliable under collinearity. The entire framework is mechanically verified with 305 Lean 4 theorems.

Key takeaway

For MLOps Engineers deploying models with correlated features, you must acknowledge that single-model SHAP rankings are inherently unstable and unreliable. Implement Dash ensemble averaging with at least 25 models to achieve stable, defensible feature importance, especially for regulatory compliance or fairness audits. Your current SHAP-based proxy discrimination audits are provably unreliable under collinearity, risking inconsistent conclusions across training runs.

Key insights

Feature ranking cannot be simultaneously faithful, stable, and complete under collinearity.

Principles

• Collinearity forces a trade-off between faithfulness, stability, and completeness.
• Rashomon property implies symmetric features are ranked oppositely by near-optimal models.
• Ensemble averaging can restore stability by reporting ties for symmetric features.

Method

Dash ensemble averaging computes consensus attribution by averaging mean absolute SHAP values from multiple independently trained models, achieving stability by sacrificing within-group completeness.

In practice

• Use a single-model screen for initial instability diagnosis.
• Confirm instability with a multi-model Z-test using 5 models.
• Resolve instability using Dash consensus with M≥25 models.

Topics

• Feature Attribution
• Explainable AI
• Model Stability
• Collinearity
• SHAP Values
• Dash Ensemble

Code references

• DrakeCaraker/dash-impossibility-lean
• DrakeCaraker/dash-shap

Best for: Research Scientist, AI Engineer, AI Product Manager, AI Scientist, Machine Learning Engineer, MLOps Engineer

Related on AIssential

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• When SHAP and LIME Fail: Lessons from Predicting Quality in the Automotive Industry — Explainability tools like SHAP and LIME have critical failure modes that can lead to misleading insights, especially with correlated data.
• Metamorphic Testing with the Rashomon Set: Explanation Faithfulness in Machine Learning — Metamorphic testing with the Rashomon Set assesses ML explanation faithfulness without ground truth.
• TN-SHAP-G: Graph-Structured Tensor Network Surrogates for Shapley Values and Interactions — TN-SHAP-G efficiently computes Shapley values for graph-structured inputs using a graph-aligned tensor network surrogate.
• What Is the Prediction Actually Made Of? — SHAP alone is insufficient for explaining retrieval-based model predictions, which require an "inner explanation" of neighbor influence.

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.LG updates on arXiv.org.